Modeling methods are used in particular in antilock control systems for motor vehicles. Such systems are known, for example, from German Patent No. 43 40 921, German Patent No. 40 12 167, or German Patent No. 40 30 724.
The braking system of a motor vehicle constitutes a hydraulic system having a master brake cylinder, brake chambers within the motor vehicle wheels, and a brake circuit connecting the master brake cylinder to the brake chambers. These components may be viewed as a plurality of reservoirs, each reservoir being fully characterized for modeling purposes by its volume, its pressure and its connections to the other reservoirs. The antilock system is a cyclically operating electronic circuit which, using a plurality of sensors, senses the pressure in the master brake cylinder and the movement characteristics of the wheels, and by actuating inlet valves arranged between the master brake cylinder and the wheel brake chambers, attempts to establish a braking pressure that permits desired wheel-movement characteristics, such as rotational speed or slip, to be achieved as precisely as possible. In order to do this, it is necessary to be able to estimate the pressure that will arise in the wheel brake chambers if the latter are connected, via the (temporary) opening of a valve, to a part of the brake circuit that is at a higher or lower pressure than the one prevailing in the wheel brake chamber before the valve is opened. Here the cyclic manner of operation of the control circuit poses the problem that only at certain time intervals can the control circuit acquire new values for the parameters it is to take into account.
The closed-loop control exercised by the circuit must remain oriented to these parameter values until new ones are available, but in fact the values of these parameters change continuously between two detection instants. The result is systematic errors in control.
If one considers two reservoirs inter-connected via a valve (see FIG. 1), the volumetric flow rate q from the higher-pressure to the lower-pressure reservoir, according to Bernoulli, is given by: EQU q=.alpha.*A(2/.rho.).sup.1/2 *.DELTA.P.sup.1/2
where .alpha. is the orifice coefficient and A is the geometric cross sectional area of the valve, .rho. is the density of the fluid and .DELTA.P is the pressure differential across the valve. If one employs this formula, or a corresponding one, to model the hydraulic system, the problem arises that only the parameter values acquired at the earlier time are available between two detection instants, whereas in the real system, the volumetric flow rate between the two detection times causes the pressure differential to even out, in turn reducing the volumetric flow rate q. Hence, too high a volumetric flow rate is always calculated in the modeling process. This causes the model to oscillate continually, restricting its utility for pressure regulation.